Selective peracetic acid determination in the presence of hydrogen peroxide using the molecular absorption properties of catalase
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1 Analyical and Bioanalyical Chemisry Elecronic Supplemenary Maerial Selecive peraceic acid deerminaion in he presence of hydrogen peroxide using he molecular absorpion properies of caalase Javier Galbán, Vanesa Sanz and Susana de Marcos
2 .- Caalase fluorescence specra fluorescence inensiy λ (nm) Fluorescence specra of ferric caalase. The bands appearing a 334 nm (exciaion) and 44 nm (emission) are characerisic of NADPH fluorescence. Caalase concenraion 5.3x -6 M in phosphae buffer. M ph 8..- Main ex equaion () deducion Before he reacion begins, he whole caalase is in Ca form: ε Ca 43, 43 [ Ca] Abs = (a) During he reacion, he oal absorbance a 43 nm will be he addiion of he hree caalase species absorbance. Abs =Abs Ca Abs Ca-I Abs Ca-II =ε Ca Ca ε Ca-I Ca I ε Ca-II Ca II (b) As [ ] [ ] [ ] 43, 43, 43, 43, Ca Ca-I Ca/Ca-I ε 43 =ε 43 =ε43 (c) and [ Ca] = [ Ca] [ Ca I] [ Ca II] (d) Combining (b) o (d) we obain: [ Ca] [ Ca II] Abs = ε ε ε Ca/Ca-I Ca-II Ca/Ca-I 43, And wih (a) Abs [ Ca II] =Abs Ca-II Ca/Ca-I [ Ca II] ε ε ==> 43, 43, Abs = ε -Abs 43, 43, Ca-II Ca/Ca-I 43 ε43
3 3.- Main ex equaion (3) deducion During he reacion, he oal absorbance a 48 nm will be he addiion of he hree caalase species absorbance. [ Ca] [ Ca I] [ Ca II] Abs =Abs Ca Abs Ca-I Abs Ca-II =ε Ca ε Ca-I ε Ca-II (e) As 48, 48, 48, 48, Ca-I Ca-II Ca-I/Ca-II ε 48 =ε 48 =ε48 (f) and [ Ca] = [ Ca] [ Ca I] [ Ca II] (d) Combining (d) o (f) we obain: [ Ca] Ca ([ Ca] [ Ca] ) [ Ca] Abs = ε ε ==> Ca-I/Ca-II 48, Abs -ε = Ca ε ε Ca-I/Ca-II 48, 48 Ca-I/Ca-II [ Ca] 4.- Maximum Ca-II concenraions for differen [] Ca-I and Ca-II concenraions a he momen a which Ca-I reaches he maximum concenraion or Ca presen is minimum concenraion ([Ca-I] max and [Ca-II] max ). Ca-II concenraion a he end of he reacion ([Ca-II] ). Reacion condiions: caalase concenraion 4x -6 M in phosphae buffer soluion. M ph 8. [], M % [Ca-I] max % [Ca-II] max % [Ca-II].69x <. <..88x x x x -5 <..4x -5 <..3x -5 6 < x -5 <..7 3
4 5.-Resoluion of he differenial equaions sysem giving he [Ca-I] min (equaion 3) and he min (equaion 4). Saring from he differenial equaion sysem and caalase mass balance: d[ca-i] = [Ca][] -[Ca-I] ( iner [Ca] ) (a) d d[ca ] = iner [Ca] [Ca-I] (b) d d[ca ] = [Ca-I] (c) d The following seps will be given: [Ca] =[Ca][Ca-I][Ca ][Ca ] ( d) ) Sysem reducion from 4 equaions o equaions By combining equaions (b) and (c) and considering ha for = [Ca ] = [Ca ] = we obain: d[ca ] iner[ca] d[ca ] ==> = [Ca ]= [Ca ] (e) d d iner[ca] In he (a) o (d) sysem, equaion (c) can be replaced by (e). Then combinaion of (d) and (e) gives: [Ca] =[Ca][Ca-I][Ca ] ==> [Ca]=[Ca] [Ca-I]-[Ca ] iner [Ca] iner [Ca] ( f ) And subsiuing (f) in (a) gives: d[ca-i] = [] [Ca] [] [Ca ] -[Ca-I] ( iner [Ca] [] ) (g) d iner [Ca] In consequence he (a) o (d) equaions sysems has been reduced o wo differenial equaion sysems consiued by equaions (b) and (g) being [Ca ] and [Ca-I] he unnowns ) Sysem reducion from equaions o equaion From equaion (b): And afer differeniaing again d[ca ] [Ca-I] = [Ca] d iner (h) 4
5 Subsiuion of (h) and (i) in (g) yields: d[ca-i] d [Ca ] = d [Ca] d iner (i) d [Ca ] d[ca ] ( iner[ca] [] ) d d [] [Ca] [Ca ] = [] [Ca] (j) iner iner Then a second order single differenial equaion is obained. 3) Solving he second order differenial equaion Equaion mahemaically belongs o he second order non-homogeneous (because he independen erms is non-zero) equaions. The general soluion of his equaion is given by: [Ca ] = [Ca ] (homogenous) [Ca ] (paricular) () The [Ca ] (paricular) is in his case: iner[] [Ca] iner[ca] [Ca ] (paricular) = = [] [Ca] [Ca] The homogeneous equaion is given by: iner iner (l) d[ca] d[ca] ( iner [Ca] [] ) [] ( iner [Ca] ) [Ca ] = (m) d d This ind of equaions are solved considering ha he soluion has he following forma: r [Ca ] = e (n ) r being a consan (see below). From (n) we obain: d[ca ] r d [Ca ] r = re (n ) = r e (n 3) d d r Replacing (n) in (m) and simplifying he e common erm r r [Ca] [] [] [Ca] = (p) iner iner By resolving he (p) second order equaion he following soluions are obained for r: r = [] (q) r = [Ca] (q) a b iner 5
6 And he homogenous equaion soluion is a linear combinaion of boh singles soluions: [] iner [Ca] [Ca ] (homogenous) = be ae (s) a and b being consan o be deermined by iniial condiions applicaion. Finally he differenial equaion soluion is obained afer replacing (s) and (l) in (): [Ca ] [Ca] be ae (u) [] ( iner[ca] ) iner = iner[ca] 4) Iniial condiions and final soluion In order o obain he final soluion parameers a and b in (u) have o be obained. To do ha he following iniial condiions were applied: Firs Iniial condiion = [Ca ] = and equaion (u) gives: Second Iniial condiion = [Ca-I] = iner[ca] = a b (v ) [Ca] iner Since (see (h)) d[ca ] d[ca ] [Ca-I] = ==> = [Ca] d d iner The applicaion of his in (u) gives: = d[ca ] d [] = [] iner[ca] b e ae ( [Ca] ) iner d[ca ] d = = b [] [Ca] a = (v ) And by combining (v) and (v) we obain: iner iner [Ca] [] a = (w ) ( [] - [Ca] - )( [Ca] ) iner iner iner[ca] b = (w ) [] - [Ca] - iner Considering (w), (w), (u) and (h): 6
7 iner ( iner[ca] ) [] [] [Ca] [Ca-I] = e e (z) [] [Ca] 5) min and [Ca-I] min calculaion Afer (z) derivaion and minimum condiions applicaion: ( iner[ca] ) ( e e ) [] iner[ca] [] d[ca-i] [] [Ca] = = d [] [Ca] iner e [] ( ) min iner min = e [Ca] [] [Ca] iner ( [Ca] ) iner min = ln (aa) [Ca] [] [] Subsiuion of (aa) in (z) gives: [Ca-I] min iner ( [Ca] ) ( [Ca] ) iner [Ca] iner [] iner ln ln [] [Ca] iner [Ca] [] [] iner [Ca] [] [] = e e ( bb) [] [Ca] iner 7
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